Panel VECM interpretation and specification I am estimating a VECM to test the causal relationship between financial development using panel data. I have four endogenous variables (GDP, 2x financial development and CPI). I am using EViews 9.
The steps I have followed are as follows (please correct me if something is not correct):


*

*Unit Root Tests = all I(1)

*Unrestricted VAR (optimal lag length selection, p)

*VAR(p) estimated, then tested for serial correlation and panel Johansen Fisher cointegration test with p-1 lags).

*Find one cointegrating vector following the trace statistic and max Eigenvalue test.

*Estimate VECM with one cointegrating vector with p-1 lags.


Here is where I have gotten a little bit stuck. In interpreting the error correction term (ECT) I find that 3 out of 4 are positive/insignificant/both. Am I right in thinking that I cannot interpret these?
Also, when it comes to assessing the specification of the model what tests are most appropriate? (Autocorrelation/Heteroskedasticity/Normality/AR Roots Graph?)    
 A: Here is an example of where three positive and one negative loading on the error correction term makes intuitive sense.
Consider a four-variable cointegrated system $(x_t, y_t, z_t, w_t)$ with $(x_t, y_t, z_t)$ being the three underlying stochastic trends and $w_t := x_t + y_t + z_t + \varepsilon_t$ where $\varepsilon_t$ is a stationary process. 
Define the error correction term as $ect_t := w_t - x_t - y_t - z_t (=\varepsilon_t)$. This is obviously stationary as $\varepsilon_t$ is stationary. 
Then it is natural to expect that the error correction term will have positive loadings in the equations for $\Delta x_t, \Delta y_t, \Delta z_t$ and a negative one in the equation for $\Delta w_t$, because:


*

*If $x_t$ deviates from the long run equilibrium by getting "too high", $ect_t$ will become negative, and then the positive loading on $ect_t$ will drag $x_{t+1}$ down, so back to equilibrium. The same holds for $y_t$ and $z_t$.

*If $w_t$ deviates from the long run equilibrium by getting "too high", $ect_t$ will become positive, and then the negative loading on $ect_t$ will drag $w_{t+1}$ down, so back to equilibrium.

*And the reverse for the cases of variables getting "too low".

